80.5.3 problem 4

Internal problem ID [18482]
Book : Elementary Differential Equations. By Thornton C. Fry. D Van Nostrand. NY. First Edition (1929)
Section : Chapter IV. Methods of solution: First order equations. section 32. Problems at page 89
Problem number : 4
Date solved : Thursday, March 13, 2025 at 12:06:23 PM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&={\mathrm e}^{z -y^{\prime }} \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 16

ode:=diff(y(z),z) = exp(z-diff(y(z),z)); 
dsolve(ode,y(z), singsol=all);
 

\[ y = \frac {\operatorname {LambertW}\left ({\mathrm e}^{z}\right )^{2}}{2}+\operatorname {LambertW}\left ({\mathrm e}^{z}\right )+c_{1} \]

✓ Mathematica. Time used: 0.023 (sec). Leaf size: 22

ode=D[y[z],z]==Exp[z-D[y[z],z]]; 
ic={}; 
DSolve[{ode,ic},y[z],z,IncludeSingularSolutions->True]
 

\[ y(z)\to \frac {1}{2} W\left (e^z\right )^2+W\left (e^z\right )+c_1 \]

✓ Sympy. Time used: 0.253 (sec). Leaf size: 17

from sympy import * 
z = symbols("z") 
y = Function("y") 
ode = Eq(-exp(z - Derivative(y(z), z)) + Derivative(y(z), z),0) 
ics = {} 
dsolve(ode,func=y(z),ics=ics)
 

\[ y{\left (z \right )} = C_{1} + \frac {W^{2}\left (e^{z}\right )}{2} + W\left (e^{z}\right ) \]